Thermal capacities and polytropic processes

TL;DR

This paper investigates the nature of thermal capacity in ideal gases, analyzing polytropic processes and clarifying whether thermal capacity functions are process, path, or state functions, with implications for physics education.

Contribution

It proposes that thermal capacity should be considered a path function and clarifies conditions under which it becomes a state function, enhancing understanding of thermodynamic processes.

Findings

Thermal capacity is tentatively a path function.

Cv and Cp are state functions only at constant volume and pressure.

The analysis clarifies thermodynamic concepts for educational purposes.

Abstract

Herein, we analyse polytropic processes for an ideal gas within the wider concept of thermal capacity. To answer the question of whether the thermal capacity is a process, path, or state function, we argue that it should be tentatively set as a path function and if it remains constant along the path, the corresponding process is polytropic. Of all the paths, there are only two, at constant volume and constant pressure, for which the thermal capacities, Cv and Cp, are state functions, i.e., system properties. The discussions herein are valuable both scientifically and instructively because they shed light on issues in undergraduate curricula that are not addressed in sufficient detail in physics textbooks, not even in the most advanced ones.